Conditional simulation for efficient global optimization

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Abstract

A classic Kriging or Gaussian process (GP) metamodel estimates the variance of its predictor by plugging-in
the estimated GP (hyper)parameters; namely, the mean, variance, and covariances. The problem is that this predictor variance is biased. To solve this problem for deterministic simulations, we propose “conditional simulation” (CS), which gives predictions at an old point that in all bootstrap samples equal the observed value. CS accounts for the randomness of the estimated GP parameters. We use the CS predictor variance in the “expected improvement” criterion of “efficient global optimization” (EGO). To quantify the resulting small-sample performance, we experiment with multi-modal test functions. Our main conclusion is that EGO with classic Kriging seems quite robust; EGO with CS only tends to perform better in expensive simulation with small samples.
Original languageEnglish
Title of host publicationProceedings of the 2013 Winter Simulation Conference (WSC 2013)
EditorsR. Pasupathy, S.-H. Kim, A. Tolk, R. Hill, M.E. Kuhl
Place of PublicationWashington DC
PublisherIEEE
Pages969-979
ISBN (Print)9781479920778
Publication statusPublished - 2013

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Kleijnen, J. P. C., & Mehdad, E. (2013). Conditional simulation for efficient global optimization. In R. Pasupathy, S-H. Kim, A. Tolk, R. Hill, & M. E. Kuhl (Eds.), Proceedings of the 2013 Winter Simulation Conference (WSC 2013) (pp. 969-979). Washington DC: IEEE.
Kleijnen, Jack P.C. ; Mehdad, E. / Conditional simulation for efficient global optimization. Proceedings of the 2013 Winter Simulation Conference (WSC 2013). editor / R. Pasupathy ; S.-H. Kim ; A. Tolk ; R. Hill ; M.E. Kuhl. Washington DC : IEEE, 2013. pp. 969-979
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title = "Conditional simulation for efficient global optimization",
abstract = "A classic Kriging or Gaussian process (GP) metamodel estimates the variance of its predictor by plugging-inthe estimated GP (hyper)parameters; namely, the mean, variance, and covariances. The problem is that this predictor variance is biased. To solve this problem for deterministic simulations, we propose “conditional simulation” (CS), which gives predictions at an old point that in all bootstrap samples equal the observed value. CS accounts for the randomness of the estimated GP parameters. We use the CS predictor variance in the “expected improvement” criterion of “efficient global optimization” (EGO). To quantify the resulting small-sample performance, we experiment with multi-modal test functions. Our main conclusion is that EGO with classic Kriging seems quite robust; EGO with CS only tends to perform better in expensive simulation with small samples.",
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Kleijnen, JPC & Mehdad, E 2013, Conditional simulation for efficient global optimization. in R Pasupathy, S-H Kim, A Tolk, R Hill & ME Kuhl (eds), Proceedings of the 2013 Winter Simulation Conference (WSC 2013). IEEE, Washington DC, pp. 969-979.

Conditional simulation for efficient global optimization. / Kleijnen, Jack P.C.; Mehdad, E.

Proceedings of the 2013 Winter Simulation Conference (WSC 2013). ed. / R. Pasupathy; S.-H. Kim; A. Tolk; R. Hill; M.E. Kuhl. Washington DC : IEEE, 2013. p. 969-979.

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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AB - A classic Kriging or Gaussian process (GP) metamodel estimates the variance of its predictor by plugging-inthe estimated GP (hyper)parameters; namely, the mean, variance, and covariances. The problem is that this predictor variance is biased. To solve this problem for deterministic simulations, we propose “conditional simulation” (CS), which gives predictions at an old point that in all bootstrap samples equal the observed value. CS accounts for the randomness of the estimated GP parameters. We use the CS predictor variance in the “expected improvement” criterion of “efficient global optimization” (EGO). To quantify the resulting small-sample performance, we experiment with multi-modal test functions. Our main conclusion is that EGO with classic Kriging seems quite robust; EGO with CS only tends to perform better in expensive simulation with small samples.

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Kleijnen JPC, Mehdad E. Conditional simulation for efficient global optimization. In Pasupathy R, Kim S-H, Tolk A, Hill R, Kuhl ME, editors, Proceedings of the 2013 Winter Simulation Conference (WSC 2013). Washington DC: IEEE. 2013. p. 969-979